Prime numbers with practical applications do get discovered. Most notably, I suppose: 2^64 - 2^32 + 1: https://cp4space.hatsya.com/2021/09/01/an-efficient-prim

Prime numbers with practical applications do get discovered. Most notably, I suppose: 2^64 - 2^32 + 1: https://cp4space.hatsya.com/2021/09/01/an-efficient-prime-for-number-theoretic-transforms/ https://cp4space.hatsya.com/2021/09/01/an-efficient-prime-fo... There are annual prizes on performing certain computations efficiently in prime fields for this prime: https://www.zprize.io/ https://www.zprize.io/ But if there is a practical application to very large primes: I don’t know. 40 million digits sounds very inefficient unless you always operate in sub-groups.